IJPAM: Volume 106, No. 3 (2016)

ON THE DYNAMICS OF A FAMILY OF RATIONAL
FUNCTIONS WHICH CONTAINS KOEBE FUNCTION

Kuldeep Prakash$^1$, R.P. Pant$^2$
$^{1,2}$Department of Mathematics
D.S.B. Campus
Kumaun University
Nainital, INDIA


Abstract. We study the dynamics of a parameterized family of quadratic rational functions $z\mapsto \lambda z/(1-z)^2$, $\lambda\in(0,\infty)$. We have investigated the dynamical and geometric properties of Julia sets and the nature of the variance of these properties according to the parameter. We have shown the Julia sets are connected when $\lambda\geqslant1$ and are dynamically defined cantor sets when $\lambda<1$. We also have shown the continuity of geometric properties specially in terms of Hausdorff dimensions of these Julia sets.

Received: November 28, 2015

AMS Subject Classification: 37F

Key Words and Phrases: Julia sets, Hausdorff dimension, bifurcation, Cantor sets

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DOI: 10.12732/ijpam.v106i3.13 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 106
Issue: 3
Pages: 873 - 881


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